Dynamic Crack Propagation in a Lattice Boltzmann Method for Solid Mechanics

Abstract

In recent years, Lattice Boltzmann methods (LBMs) have been adapted and developed to simulate the behavior of solids. They have already been applied to fractures as well. However, until now, our previous work has been restricted to stationary cracks.In this work, we regard the reduced 2D case of anti-plane shear deformation with mode III crack opening. The wave equation is the governing equation for this problem, which is solved via an LBM.The main contribution of this work is the introduction of an algorithm to handle crack growth in an LBM for solids. The underlying scheme is based on geometric assumptions, which is well suited for the regular lattice used by the LBM. A fracture criterion based on the stress intensity factor is implemented and illustrated by a numerical example.

On dynamic crack propagation in a lattice Boltzmann method for elastodynamics in 2D

“…This is also favourable for the simulation of cracks. An LBM for solids has already been applied to crack propagation [6,7], where the proof-of-concept was given for mode III cracks, albeit in rather reduced mechanical and numerical setting. The same algorithm is used now with modifications due to the different boundary conditions.…”